Power and Distribution Transformers. Practical Design Guide

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgments
Author
Chapter 1 Transformer Design
	1.1 Introduction
	1.2 Definition of Transformer
	1.3 Design Objectives
	1.4 Basic Theory of Transformer
		1.4.1 Electromagnetic Terms and Concepts
		1.4.2 Charges, Electric Field and Magnetic Field
		1.4.3 Maxwell’s Equations
	1.5 Power Transfer Capacity of Transformer
Chapter 2 Brief History of Transformers and the Emerging Trends
	2.1 Brief History of the Transformer
	2.2 Development of Materials for Transformer production
		2.2.1 Conducting Material
		2.2.2 Cooling Medium
		2.2.3 Magnetic Material (Electrical Steel)
		2.2.4 New and Emerging Technologies
		2.2.5 New Technologies in Commercial Use
			2.2.5.1 Amorphous Core Transformers
			2.2.5.2 Symmetrical Wound Core (3D Core) Transformer
			2.2.5.3 Biodegradable Oil-Filled Transformer
			2.2.5.4 Gas-Insulated Transformers
		2.2.6 Application of Emerging Technologies to Transformer Design and Manufacture ??
			2.2.6.1 Transformers Using High-Temperature Superconductors
			2.2.6.2 Intelligent Transformer for Smart Grid
	2.3 Replacement of Copper/Aluminium by Carbon Nanotube
	2.4 Use of Artificial Intelligence (AI) for Transformer Design and Diagnostics
	2.5 Use of Additive Manufacturing (3D Printing) for Transformer Production
Chapter 3 Design Procedures
	3.1 Design Input Data
	3.2 Design Flow Chart [For Design with LV Parallel Conductors and HV Layer Windings]
Chapter 4 Core Design: Core Area Calculation
	4.1 Calculation of Core Diameter and Core Area
		4.1.1 Selection of Core Circle
		4.1.2 Selection of Core Step Widths
			4.1.2.1 Optimum Width of Core Steps to Get Maximum Core Area
		4.1.3 Calculation of Gross Area and Net Area of Core
Chapter 5 Winding Design
	5.1 Calculation of Volts per Turn
	5.2 Calculation of Phase Volts and Phase Currents
	5.3 Calculation of Number of Turns
		5.3.1 Calculation of Voltage and Turns of Extended Delta Winding
		5.3.2 Calculation of Tap Turns
			5.3.2.1 Categories of Voltage Variation
	5.4 Calculation of the Cross Section Area of Conductor
	5.5 Selection of Current Density
	5.6 Selection of Conductor Sizes
	5.7 Selection of Types of Windings
	5.8 Tap CHANGERS and Tap Changer Connections
		5.8.1 Off-Circuit Tap Changer
		5.8.2 Off-Load Tap Changer
		5.8.3 On-Load Tap Changer
	5.9 Calculation of Axial Height of Winding
		5.9.1 Spiral Winding
		5.9.2 Foil Winding
		5.9.3 Crossover Coils
		5.9.4 Disc Winding
	5.10 Electrical Clearances of Oil-Filled Three-Phase Transformers
	5.11 Calculation of Electrical Stresses for Different Configurations
		5.11.1 Two Bare Uniform Electrodes (Parallel Electrodes) (One Dielectric) ?
		5.11.2 Multidielectric (Parallel Electrodes)
		5.11.3 Concentric Cylindrical Electrodes (One Dielectric)
		5.11.4 Concentric Cylindrical Electrodes with Multiple Dielectrics
		5.11.5 Cylindrical Conductor to Plane Electrode
		5.11.6 Insulated Cylindrical Conductor to Plane Electrode
		5.11.7 Factors Affecting Insulation Strength
	5.12 Insulation between Layers
	5.13 Calculation of Winding Diameter and Radial Depth
	5.14 Weight of Bare Conductor, Covered Conductor and Resistance of Winding
Chapter 6 Calculation of Load Loss
	6.1 Calculation of I 2R Loss
	6.2 Calculation of Eddy Current Losses and Stray Losses
		6.2.1 Eddy Current Loss in Winding
		6.2.2 Stray Loss in Bushing plate
		6.2.3 Stray Losses in Flitch Plate (Tie Plate)
		6.2.4 Circulating Current Loss in Continuous Disc Winding
		6.2.5 Empirical Formula for Tank Loss Calculation
		6.2.6 Loss on Transformer Tank Due to High-Current Busbars
		6.2.7 Empirical Formula for Calculating Total Stray Loss
	6.3 Calculation of Load Loss
Chapter 7 Calculation of Reactance
	7.1 Reactance Calculation of Two-Winding Transformer
		7.1.1 Alternate Formula for Reactance Calculation
	7.2 Reactance Calculation of Zigzag Connected two-winding Transformers
		7.2.1 Effective Reactance of Zigzag Connected Transformers
	7.3 Reactance Calculation with Different Ampere-Turn Distributions
		7.3.1 LV–HV–LV Arrangement or Similar
		7.3.2 Winding with Ducts inside or Windings Made in Two Separate Layers with Gaps
		7.3.3 Reactance of Layer Winding with Reduced Layer Height towards Outer Layers
	7.4 Reactance Calculations Based on Total Inductance
	7.5 Reactance Calculation of Extended Winding
	7.6 Zero Sequence Impedance of Zigzag Earthing Transformer
	7.7 Reactance Calculation of Neutral Earthing Transformer with Auxiliary Winding
	7.8 Reactance of Autotransformer with Tertiary Winding
	7.9 Effective Reactance of Windings in Series (Autotransformer)
	7.10 Reactance Calculation of Split Winding
	7.11 Calculation of Reactance of Individual Windings
	7.12 Calculation of Reactance by Finite Element Method
	7.13 Zero Sequence Impedance of Three-Phase Transformers
	7.14 Zero Sequence Impedance Calculation
Chapter 8 Calculation of Core Frame Size, Core Losses, Efficiency and Regulation
	8.1 Core Frame Size and Core Weight Calculation
	8.2 Core Loss Calculation
		8.2.1 Loss Calculation Based on Average Building Factor
		8.2.2 Loss Calculation by Adding of Losses Across the Grain and Along the Grain
	8.3 Specific Losses of Different Grades of CRGO Materials
	8.4 Core Losses of Symmetrical Core Transformers
		8.4.1 Advantages of Symmetrical Wound Core
		8.4.2 Manufacturing Process of Symmetrical Wound Core
		8.4.3 Symmetrical Wound Core Designs
	8.5 Calculation of No-Load Current (Excitation Current)
	8.6 Suggested Changes of Design Parameters to Get Desired Losses
	8.7 Calculation of Efficiency and Regulation
		8.7.1 Calculation of Efficiency
			8.7.1.1 Calculation of Efficiency as per ANSI Standard
			8.7.1.2 IEC 60076 Standard and ANSI C57.12 Standard
			8.7.1.3 Calculation of Efficiency as per IEC 60076 and ANSI C57.12
		8.7.2 Calculation of Regulation
	8.8 Calculation of Equivalent Circuit Parameters of Transformer
Chapter 9 Lightning and Switching Surges on Transformers
	9.1 Introduction
	9.2 Effect of Surges on Transformer Winding
	9.3 Capacitive Equivalent Circuit of Transformer
	9.4 Calculation of Capacitances
	9.5 Calculation of Initial Voltage Distribution of a Capacitive Ladder Circuit
	9.6 Impulse and Switching Surge Waves as per IEC 60076-4
	9.7 Simulation of Waveform for Analytical Calculations
	9.8 Design Techniques to Reduce Non-linear Impulse Voltage Distribution
	9.9 Power Frequency Breakdown and Impulse Breakdown
	9.10 Selection of Surge Arrester for Transformer
		9.10.1 Surge Arresters Parameters
		9.10.2 Calculation of Arrester Rating of Solidly Grounded three-Wire System
Chapter 10 Inrush Current in Transformers
	10.1 Introduction
	10.2 Problems of Transformer Inrush Current
		10.2.1 Mechanical Stresses
		10.2.2 Overvoltage Due to Harmonic Resonance
		10.2.3 Nuisance Tripping of Transformer
		10.2.4 Temporary Voltage Dip
		10.2.5 Sympathetic Inrush
	10.3 Calculation of Inrush Current
		10.3.1 Approximate Value of the First Peak of Inrush Current
		10.3.2 First Peak of Inrush Current Considering Switching Angle and Circuit Resistance
		10.3.3 Estimation of Initial Few Peaks of Inrush Current
		10.3.4 Calculation Example
	10.4 Frequency Range of Inrush Current and Other Transients
	10.5 Influence of Design on Inrush Current
	10.6 Methods for Reduction of Inrush Current
	10.7 Effect of System and Switching Parameters on Inrush Current
		10.7.1 Source Resistance
		10.7.2 Switching Angle
		10.7.3 Effect of Remnant Flux on the First Cycle Peak Current
Chapter 11 Calculation of Core and Coil Assembly Dimensions, Tank Size and Tank Weight
	11.1 Calculation of the Dimensions of Core and Coil Assembly (CCA)
	11.2 Calculation of Dimensions of Tank
	11.3 Calculation of the Size of Wooden Beam (Core Clamp)
	11.4 Calculation of Weight of Tank [Radiator-Type Tank]
		11.4.1 Weight of Top Cover
		11.4.2 Weight of Sidewalls
		11.4.3 Bottom Plate
		11.4.4 Tank Curb
		11.4.5 Horizontal Stiffeners
		11.4.6 Vertical Stiffeners
		11.4.7 Base Channel
	11.5 Design of Conservator
		11.5.1 Size of the Conservator
	11.6 Air Cell for Conservator
	11.7 Dehydrating Breathers for Transformers
		11.7.1 Regeneration of Saturated Silica Gel
		11.7.2 Design Parameters of Breather
		11.7.3 Calculation of Quantity of Silica Gel Required
		11.7.4 Self-Dehydrating Breather
		11.7.5 Calculation of Desiccant in Breather Alternate Method
Chapter 12 Calculation of Winding Gradient, Heat Dissipation Area and Oil Quantity
	12.1 Radiation and Convection from Surface
	12.2 Heat Dissipation Data for Radiator
	12.3 Calculation of Winding Gradient
	12.4 Calculation of Winding Gradient: Alternate Method
	12.5 Calculation of Mean Oil Temperature Rise
	12.6 Calculation of Weight of Radiator Panels
	12.7 Calculation of Weight of Corrugated Fins
	12.8 Effect of Ambient Temperature on the Top Oil Temperature Rise
	12.9 Heat Dissipation by Forced Air Cooling
	12.10 Reference Ambient as per IEC
	12.11 Calculation of Weighted Average Ambient Temperature
	12.12 Calculation of Oil Quantity
Chapter 13 Calculation of Pressure Rise, Stresses and Strength of Tank
	13.1 Calculation of Pressure Rise in Sealed Tanks
		13.1.1 Tank with Pressed Steel Radiators with Air/Gas Cushion
		13.1.2 Corrugated Tank with Air/Gas Cushion
		13.1.3 Corrugated Tank with Complete Filling of Oil (No Air/Gas Cushion)
	13.2 Calculation of Pressure and Stresses on Corrugated Fins for Completely Filled Transformer
	13.3 Gas Pressure Calculation of Sealed Transformers, Considering Solubility Changes of Gas with Temperature and Pressure
	13.4 Calculations of Strength of Rectangular Tank When Pressure Tested
		13.4.1 Tank Dimensions and Constants
		13.4.2 Calculation of Section Modulus Required for Stiffeners
	13.5 Fastener Spacing and Tightening Torque of Gasket Joints of Oil-Filled Transformers
		13.5.1 Introduction
		13.5.2 Leakage Rate through Gasket Joint
		13.5.3 Properties of Gasket Required for a Good Joint
		13.5.4 Types of Gaskets Used and Comparison of Properties
		13.5.5 Fastener Spacing
		13.5.6 Bolt Torque
		13.5.7 Joining/Splicing of the Gasket
		13.5.8 Thickness of Gaskets for Distribution Transformers
Chapter 14 Calculation of the Short Circuit Forces and Strength of Transformers
	14.1 Introduction
	14.2 Calculation of Thermal Ability to Withstand Short Circuits
	14.3 Ability to Withstand the Dynamic Effect of Short Circuits
	14.4 Design Review and Evaluation
		14.4.1 Comparative Evaluation with a Type-Tested Transformer of Similar Design
		14.4.2 Evaluation by Check Against the Manufacturer’s Design Rules for Short Circuit Strength
Chapter 15 Rectifier Transformers
	15.1 Winding Arrangements and Harmonics Produced
	15.2 Calculation of the Number of Turns When Extended Star or Extended Delta Winding Is Used
	15.3 Calculation of the Number of Turns of Polygon Delta Connection with Vector Group Pd0[sub(+7.5)] (7.5° lag)
	15.4 Determination of the Phase Displacement and Ratio by Single-Phase Turns Ratio Measurement
	15.5 Calculation of Ratio and Phase Angle Error
	15.6 Transformers for Variable-Speed Drives (VSDs)
	15.7 Effect of Winding Geometry on Load Losses
	15.8 Calculation of Load Loss
	15.9 Duty Cycles for Different Applications
	15.10 Design Example of a Rectifier Transformer with Three Secondaries
Chapter 16 Cast Resin Transformers
	16.1 Basic Design Parameters
		16.1.1 Maximum Electrical Stresses
		16.1.2 Insulation Design
			16.1.2.1 Clearances to Enclosure and Live Parts
			16.1.2.2 Clearance between Windings, Core, Etc
			16.1.2.3 Clearance between Tap Links, Line Terminals to Tap Link, Etc
	16.2 Calculation of Technical Parameters
		16.2.1 Core Temperature Rise Calculation
		16.2.2 Temperature Rise of Winding
		16.2.3 Overload Capacity – For AN Cooling
		16.2.4 Altitude Correction Factor
	16.3 Typical Resin System for Class F applications
		16.3.1 General Class F Filled System
		16.3.2 Typical Resin System for Class H Applications
	16.4 Enclosure for Cast Resin Transformers
		16.4.1 The Air Inlet Area Required
		16.4.2 Standard Clearances to Enclosure
	16.5 Calculation of Time Constant of Dry-Type Transformers
		16.5.1 Time Constant of Winding at Rated Load
		16.5.2 Time Constant at Any Loading
	16.6 Ageing and Transformer Insulation Life Expectancy
	16.7 Design Using Round/Rectangular Conductor
		16.7.1 Introduction
		16.7.2 Conductor Insulation for Class F System
		16.7.3 Layer Winding Arrangement
			16.7.3.1 LV Winding
			16.7.3.2 HV Winding
	16.8 Calculation of Cooling Fan Capacity
	16.9 Ventilation of the Transformer Room
	16.10 Effect of the Enclosure IP Class on Temperature Rise
	16.11 Temperature Rise of an Transformer with IP54 Enclosure
	16.12 Anti-vibration Pads
	16.13 RC Snubber for Cast Resin Transformers
Chapter 17 Earthing Transformers
	17.1 Introduction
	17.2 Basis of Rating
	17.3 Rated Short-Time Neutral Current Duration and Continuous Current
	17.4 Fault Current Flow through Earthing Transformers
	17.5 Calculation of Zero Phase Sequence Impedance (ZPS)
	17.6 Design of Earthing Transformers
		17.6.1 Calculation of Maximum Permissible Current Density
		17.6.2 Equivalent kVA for an Earthing Transformer
	17.7 Design of an ONAN Earthing Transformer without Auxiliary Winding
		17.7.1 Sample Design of an Earthing Transformer without Auxiliary Winding
		17.7.2 Calculation of the Short-Time Current Density
		17.7.3 Winding Design
	17.8 Design of an ONAN Earthing Transformer with Auxiliary Winding
	17.9 Rated Short-Time Temperature Rise
Chapter 18 Amorphous Core Transformers
	18.1 Introduction
	18.2 Design Procedure of Amorphous Wound Core
		18.2.1 Structure of Core
	18.3 Design of a Single-Phase Amorphous Core Transformer
		18.3.1 Core Dimensions
		18.3.2 Core Coil Assembly Dimensions and Clearances
	18.4 Minimum Clearance Required for Amorphous Core Transformers
	18.5 Typical Core Loss (w/kg) and Excitation Current (VA/kg) of an Amorphous Core
		18.5.1 Amorphous Core Losses and VA/kg at 50 and 60 Hz (Grade 2605HB1M)
		18.5.2 Amorphous Core – Losses and VA/kg at 50 and 60 Hz (Grade 2605SA1)
	18.6 Calculation of Mean Length of Wound Core
	18.7 Calculation of Mean Length of Windings with Wound Core
	18.8 Reactance Calculation
	18.9 Design Example of a 15-kVA Single-Phase Amorphous Core Transformer
	18.10 Design Example of a 3-Phase Amorphous Core Transformer
Chapter 19 Design of Current-Limiting Reactors
	19.1 Air-Core Dry-Type Reactors
		19.1.1 Magnetic Field Produced by a Cylindrical Winding
		19.1.2 Eddy Current Losses Produced by Metallic Parts
		19.1.3 Clearances Required for Air-Core Reactors
		19.1.4 Design Procedure of Dry Type Air Core Series Reactors
		19.1.5 Sample Calculations of a Single Phase Air Core Dry Type Reactor Coil
			19.1.5.1 Equalization of Current Sharing between Parallel Layers
			19.1.5.2 Cooling Calculation
	19.2 Oil-Filled Air-Core Reactors
		19.2.1 Introduction
		19.2.2 Design Procedure of Air Core Oil Filled Reactors
		19.2.3 Selection of Conductor Dimensions
		19.2.4 Calculation of the Dimensions of the Shield
	19.3 Design of Oil-Filled Gapped-Core Reactors
Chapter 20 Scott-Connected Transformers
	20.1 Basic Theory
	20.2 Connection Diagram and Current Distribution
	20.3 Le Blanc Connection
	20.4 Application of Scott-Connected Transformers
	20.5 Example of Scott-Connected Transformer Winding Design
Chapter 21 Autotransformers
	21.1 Introduction
	21.2 Current Distribution in the Windings of an Autotransformer
	21.3 Auto Connection of 3-Phase Transformers
	21.4 Tertiary Winding of an Autotransformer
		21.4.1 Design Features of a Tertiary Winding
		21.4.2 Eliminating the Tertiary Winding
	21.5 Location of Tap Changer of Autotransformers
		21.5.1 Direct Voltage Variation and Indirect Voltage Variation
	21.6 Effect of Geometrical Arrangement of Tap Winding of Autotransformers
	21.7 Design of a 50–MVA, 132/66-kV Autotransformer
Chapter 22 Transformers for Special Applications or Special Designs
	22.1 Transformers for Use in Explosive Atmospheres [ATEX-/IECEx-Certified Transformers]
		22.1.1 Introduction
		22.1.2 Equipment Coding as per ATEX Marking
		22.1.3 Transformer Design Consideration to comply with ATEX Certification Requirement
	22.2 Furnace Transformers
		22.2.1 Introduction
		22.2.2 Design Features of Furnace Transformers
	22.3 Multiwinding Transformers
		22.3.1 Introduction
		22.3.2 Three-Winding Transformers
		22.3.3 Four-Winding Transformers (1 Input and 3 Output Windings)
		22.3.4 Five-Winding Transformers (1 Input and 4 Output Windings)
	22.4 Design of Dual-Ratio Transformers
		22.4.1 Introduction
		22.4.2 Design of Transformers with Dual Ratio on the Primary Side
			22.4.2.1 22–11 kV Connection on the Primary
			22.4.2.2 33–11 kV Series-Parallel Connection
			22.4.2.3 11–6.6 kV Connection
	22.5 Liquid-Filled Transformers Using High-Temperature Insulation Materials
		22.5.1 Introduction
		22.5.2 Thermal Class of Insulation Materials
		22.5.3 Concept of High-Temperature Insulation
		22.5.4 Design Parameters to be Considered
		22.5.5 Thermal Class and Parameters of High-Temperature Insulation Materials
			22.5.5.1 Typical Enamel Insulation for Winding Conductor
			22.5.5.2 Insulation Liquids
	22.6 Traction Transformers
		22.6.1 Introduction
		22.6.2 Design Features of On-Board Traction Transformers
			22.6.2.1 Specifications and General Requirements
			22.6.2.2 Harmonics
		22.6.3 Design of Transformers
			22.6.3.1 Core
			22.6.3.2 Windings
			22.6.3.3 Insulation Design
			22.6.3.4 Cooling System
	22.7 Symmetrical Core Transformers (Tridimensional Core)
		22.7.1 Design of Symmetrical Core Transformers
			22.7.1.1 Design of Transformers
Chapter 23 Transformers for Renewable Energy Applications
	23.1 Introduction
	23.2 Transformers for Distributed Photovoltaic Generation
		23.2.1 Special Design Features Required to Meet the Service Conditions
	23.3 Transformers for Wind Turbine
	23.4 Emerging Trends in the Development of Transformers for Renewable Energy
Chapter 24 Condition Monitoring of Oil-Filled Transformers
	24.1 Online and Off-Line Diagnostic Methods
	24.2 Online Monitoring Methods
	24.3 Off-Line Diagnostic Methods
	24.4 Dissolved Gas Analysis
	24.5 Partial Discharge MEASUREMENT
	24.6 Furan Analysis and Degree of Polymerization of Transformers
	24.7 Sweep Frequency Analysis
	24.8 Dielectric Frequency Response Analysis
	24.9 Recovery Voltage Measurement
	24.10 Other Monitoring and Diagnostic Methods
		24.10.1 Optical Spectroscopy
		24.10.2 Search Coil–Based Online Diagnostics of Transformer Internal Faults
		24.10.3 Polarization and Depolarization Current Test
		24.10.4 Embedded Wireless Monitoring and Fault Diagnostic System
		24.10.5 Frequency Domain Spectroscopy
		24.10.6 Monitoring of Temperature
		24.10.7 Load Monitoring
		24.10.8 Vibration Monitoring
		24.10.9 Monitoring of the Functioning of Bushings and On-Load Tap Changer
	24.11 Fuzzy Information Approach for Interpretation of Results of Different Diagnostic Methods
Chapter 25 Carbon Footprint Calculation of Transformer
	25.1 Introduction
	25.2 Carbon Footprint Calculation Flowchart
	25.3 Performance Parameters of the Transformers Considered for the Calculation
		25.3.1 Raw Materials for Production
		25.3.2 Transport of Raw Materials
		25.3.3 Manufacture of Components and Subassemblies
		25.3.4 Transport of Components and Subassemblies
		25.3.5 Manufacture of the Product
		25.3.6 Transportation of Product
		25.3.7 Installation of Product
		25.3.8 Operation (Usage) of the Product
		25.3.9 Disposal and Recycling at the End of Life
	25.4 Total Lifetime Carbon Footprint of 1000-kVA Transformers
Chapter 26 Seismic Response Calculation for Transformers
	26.1 Introduction
	26.2 Intensity and Seismic Zones
	26.3 Response Spectrum
	26.4 Calculation Method as per Uniform Building Code
	26.5 Design of Anchor Bolt
	26.6 Calculation of Natural Frequency of Vibration of Transformer
	26.7 Seismic Qualifications Method as Per Clause D-3 IEEE 693
	26.8 General Seismic Capability Calculation
		26.8.1 Standard Amplitude Method
		26.8.2 Calculated Amplitude Method
	26.9 Anchor Bolt Design Considering Static, Wind and Seismic Loads
		26.9.1 Static Load – D
		26.9.2 Wind Load – W
		26.9.3 Seismic Load – E
	26.10 Seismic Qualification Testing of Transformer
		26.10.1 Shake Table Testing
		26.10.2 Response Spectra
		26.10.3 Test Procedure
		26.10.4 Acceptance Criteria and Test Report
Chapter 27 Solid-State Transformer
	27.1 Introduction
	27.2 Design Features of the Transformer for Smart Grid
	27.3 Design of a 11kV/415V Three-Phase Solid-State Transformer
		27.3.1 Basic Structure
		27.3.2 Design of Module 1: (MV AC to DC)
		27.3.3 Design of Module 2
		27.3.4 Design of Module 3
		27.3.5 Design of Module 4 (Low-Voltage Rectifier)
		27.3.6 Design of Module 5 – (Low-Voltage Inverter)
	27.4 Design of Medium-Frequency Transformer
	27.5 Winding Design
		27.5.1 Winding Arrangement
		27.5.2 Calculation of Load Losses
		27.5.3 Insulation Design
		27.5.4 Cooling Design
	27.6 Materials Required for Solid-State Transformers
		27.6.1 Active Power Conversion Materials (Semiconductors)
		27.6.2 Magnetic Materials
		27.6.3 Conducting Materials
		27.6.4 Insulation Materials and Other Parts
Chapter 28 Transformer Design Optimization
	28.1 Introduction
	28.2 Objective Functions for Design Optimization
		28.2.1 Optimization of Lowest Initial Material Cost
		28.2.2 Lowest Initial Product Cost
		28.2.3 Lowest Total Owning Cost
		28.2.4 Lowest Total Owning Cost Including the Cost of Lifetime CO2 Emission
	28.3 Constraints of Design Optimization
	28.4 Design Optimization Methods
		28.4.1 Brute Force Method
		28.4.2 Optimum Design of Distribution Transformers
			28.4.2.1 When Upper Limits of No-Load Loss and Load Loss Are Specified
			28.4.2.2 When Capitalizations of No-Load Loss and Load Loss Are Specified
			28.4.2.3 Derivation of Parameters of Objective Function
			28.4.2.4 Derivation of Equations
		28.4.3 Genetic Algorithms
		28.4.4 Harmony Search Algorithm
		28.4.5 Other Optimization Techniques
			28.4.5.1 Simulated Annealing
			28.4.5.2 Tabu Search Algorithm
			28.4.5.3 Swarm Intelligence
Chapter 29 Corrosion Protection
	29.1 Typical Painting Systems for Transformer Tanks and Radiators
	29.2 Design Life (Durability) of the Coating System
	29.3 Painting Criterion
		29.3.1 Painting of Internal Areas (Air filled)
		29.3.2 Painting of Internal Oil Filled Areas
	29.4 Tin Coating (Electrodeposited Coating of Tin)
	29.5 Zinc Coating on Iron or Steel
Chapter 30 Calculation of Miscellaneous Technical Parameters
	30.1 Overloading of Oil-Immersed Transformers
		30.1.1 Introduction
		30.1.2 Loss of Life of Insulation
		30.1.3 Effects of Loading above the Rated Load
		30.1.4 Categories of Overloading
			30.1.4.1 Normal Cyclic Loading
			30.1.4.2 Long-Time Emergency Loading
			30.1.4.3 Short-Time Emergency Loading
		30.1.5 Calculation of Hot Spot Temperature and Top Oil Temperature
	30.2 Altitude Correction Factors
		30.2.1 Correction Factor for Temperature Rise
		30.2.2 Correction Factors for External Clearances
		30.2.3 Altitude Correction Factor as Per CIGRE Report 659—June 2016 (Transformer Thermal Modelling)
	30.3 Effect of Solar Radiation on the Temperature Rise of Oil-Filled Transformers
		30.3.1 Solar Radiation
		30.3.2 Solar Radiation on the Surface of the Transformer
		30.3.3 Calculation of the Effect of Solar Radiation on Oil Temperature Rise and Winding Temperature Rise
	30.4 Circulating Current in Transformer
		30.4.1 Introduction
		30.4.2 Circulating Current in Tank
		30.4.3 Circulating Current Across Tank Band
		30.4.4 Circulating Current in Winding with Parallel Conductors
		30.4.5 Circulating Current in Core Clamping Frame
		30.4.6 Circulating Current from the Tank to Earth
		30.4.7 Circulating Current from Core Laminations
		30.4.8 Circulating Current from Geomagnetically Induced Currents
	30.5 Electrical and Magnetic Fields Outside the Transformers
		30.5.1 Electric Field
		30.5.2 Magnetic Field
	30.6 Fault Current of Transformers
	30.7 Conversion of Losses, Impedance and Noise Level Measured at 50 Hz for Transformers Designed For 60 Hz and Vice Versa
		30.7.1 Introduction
		30.7.2 Conversion Factors for No-Load Losses and No-Load Current
		30.7.3 Impedance of Transformer
		30.7.4 Conversion Factors for Load Loss
		30.7.5 Conversion Factor for Sound Level
	30.8 IEC Rating of Transformer Designed for Operation at Higher than IEC Ambient Temperature
	30.9 Heat Dissipation from Steel Prefabricated Substation
	30.10 Transformer Rating for Supplying Nonsinusoidal Load
	30.11 Fuses for Transformer Protection
	30.12 Transformer Sound Level
		30.12.1 Introduction
		30.12.2 Determination of Sound Level
		30.12.3 Sources of Sound from a Transformer
		30.12.4 Calculation of Sound Level of Transformer
		30.12.5 Design Methods to Reduce Sound Level of Transformer
			30.12.5.1 Reduction of Sound Level from Core
			30.12.5.2 Reduction of Sound from Winding
			30.12.5.3 Other Methods for Reducing Sound Level
		30.12.6 Other Factors Affecting Sound Level of Transformer
			30.12.6.1 DC Bias in Magnetization
			30.12.6.2 Harmonics in Load Current
	30.13 Design of Connection Bus Bars inside Transformers
		30.13.1 Permissible Current in a Bus Bar
		30.13.2 Short-Time Thermal Capability of Bus Bar
		30.13.3 Natural Frequency of Bus Bar
		30.13.4 Short-Circuit Force between Bus Bars
		30.13.5 Mechanical Strength of Bus Bar under Short Circuit
	30.14 Calculation of Wind Load on Transformer
		30.14.1 Introduction
		30.14.2 Factors Affecting the Wind Load
		30.14.3 Surface Roughness Coefficient
		30.14.4 Topography Coefficient
		30.14.5 Wind Velocity Calculation
		30.14.6 Maximum Wind Load on a Surface
		30.14.7 Example of Wind Load Calculation
A.1 Design of 1000 kVA, 11/0.4 kV, ONAN Transformer
A.2 Design of 20 MVA, 33/11.5 kV, ONAN Transformer
A.3 Design of 72/90 MVA, 132/34.5 kV, ONAN/ONAF Transformer
A.4 Finite Element Methods for Transformer Design
A.5 Total Owning Cost (TOC) of a Transformer
A.6 Comparison of IEC 60076 and ANSI/IEEE C.57.12 Standards
Bibliography
Index